Question

The population of a particular town 4 years back was 2,500. The current population
is 4,000.
What will be the population after a period of 4 years, if the rate of growth of the
population has been kept constant and it has been compounded annually?​

Answer 1

Given :  The population of a particular town 4 years back was 2,500. The current population  is 4,000.  the rate of growth of the  population has been kept constant and it has been compounded annually

To find : What will be the population after a period of 4 years

Solution:

Let say rate of growth = r % per annum

A = P(1 + r/100)ⁿ  as rate of growth of the  population has been kept constant and it has been compounded annually

Population 4 years back   = 2500

Time period n = 4 years

Current population = 2500 ( 1 + r/100)⁴

=> 4000 = 2500 ( 1 + r/100)⁴

=>  ( 1 + r/100)⁴ = 1.6

Current population = 4000

Population after 4 years = 4000 ( 1 + r/100)⁴

Substitute ( 1 + r/100)⁴ = 1.6

=> Population after 4 years = 4000 * 1.6

=> Population after 4 years = 6400

population after a period of 4 years = 6400

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